[LeetCode] Minimum Size Subarray Sum 最短子数组之和

题意

Given an array of n positive integers and a positive integer s, find the minimal length of a subarray of which the sum ≥ s. If there isn't one, return 0 instead.

For example, given the array [2,3,1,2,4,3] and s = 7,
the subarray [4,3] has the minimal length under the problem constraint.

click to show more practice.

More practice:
If you have figured out the O(n) solution, try coding another solution of which the time complexity is O(n log n).

Credits:
Special thanks to @Freezen for adding this problem and creating all test cases.

这道题给定了我们一个数字，让我们求子数组之和大于等于给定值的最小长度，跟之前那道 Maximum Subarray 最大子数组有些类似，并且题目中要求我们实现O(n)和O(nlgn)两种解法，那么我们先来看O(n)的解法，我们需要定义两个指针left和right，分别记录子数组的左右的边界位置，然后我们让right向右移，直到子数组和大于等于给定值或者right达到数组末尾，此时我们更新最短距离，并且将left像右移一位，然后再sum中减去移去的值，然后重复上面的步骤，直到right到达末尾，且left到达临界位置，即要么到达边界，要么再往右移动，和就会小于给定值。代码如下：

思路

这道题需要比较巧妙的思考，不能直接蛮干，比如说移动窗口，再更新它的窗口最小长度；或者先计算累计和，通过加上给定的值，去得到窗口信息，再更新最小长度。

实现

移动窗口

// O(n)
class Solution {
public:
    int minSubArrayLen(int s, vector<int>& nums) {
        if (nums.empty()) return 0;
        int left = 0, right = 0, sum = 0, len = nums.size(), res = len + 1;
        while (right < len) {
            while (sum < s && right < len) {
                sum += nums[right++];
            }
            while (sum >= s) {
                res = min(res, right - left);
                sum -= nums[left++];
            }
        }
        return res == len + 1 ? 0 : res;
    }
};

同样的思路，换另外一种写法

class Solution {
public:
    int minSubArrayLen(int s, vector<int>& nums) {
        int res = INT_MAX, left = 0, sum = 0;
        for (int i = 0; i < nums.size(); ++i) {
            sum += nums[i];
            while (left <= i && sum >= s) {
                res = min(res, i - left + 1);
                sum -= nums[left++];
            }
        }
        return res == INT_MAX ? 0 : res;
    }
};

二分法

// O(nlgn)
class Solution {
public:
    int minSubArrayLen(int s, vector<int>& nums) {
        int len = nums.size(), sums[len + 1] = {0}, res = len + 1;
        for (int i = 1; i < len + 1; ++i) sums[i] = sums[i - 1] + nums[i - 1];
        for (int i = 0; i < len + 1; ++i) {
            int right = searchRight(i + 1, len, sums[i] + s, sums);
            if (right == len + 1) break;
            if (res > right - i) res = right - i;
        }
        return res == len + 1 ? 0 : res;
    }
    int searchRight(int left, int right, int key, int sums[]) {
        while (left <= right) {
            int mid = (left + right) / 2;
            if (sums[mid] >= key) right = mid - 1;
            else left = mid + 1;
        }
        return left;
    }
};

这个解法要用到二分查找法，思路是，我们建立一个比原数组长一位的sums数组，其中sums[i]表示nums数组中[0, i - 1]的和，然后我们对于sums中每一个值sums[i]，用二分查找法找到子数组的右边界位置，使该子数组之和大于sums[i] + s，为什么要加上s呢，因为前面我们已经计算出了加上数组前面的和，那么我们只需要判断当前的值加上s等于后面的哪个值，就可以得出后面的值的下标，其实那个s就是前面和后面之间的原数组的值的和，然后我们更新最短长度的距离即可。

或者不需要新加一个函数

class Solution {
public:
    int minSubArrayLen(int s, vector<int>& nums) {
        int res = INT_MAX, n = nums.size();
        vector<int> sums(n + 1, 0);
        for (int i = 1; i < n + 1; ++i) sums[i] = sums[i - 1] + nums[i - 1];
        for (int i = 0; i < n; ++i) {
            int left = i + 1, right = n, t = sums[i] + s;
            while (left <= right) {
                int mid = left + (right - left) / 2;
                if (sums[mid] < t) left = mid + 1;
                else right = mid - 1;
            }
            if (left == n + 1) break;
            res = min(res, left - i);
        }
        return res == INT_MAX ? 0 : res;
    }
};

总结

看来并不能直接看别人的说的去实现，还是要自己去理解才行，每个人有每个人自己的理解。